Space transit simulator planetarium

ABSTRACT

A planetarium capable of simulating planet, sun and moon movements and changes as viewed from outside of, as well as within, cis-lunar space as provided by a star field projector preferably capable of projecting a selected portion of the celestial sphere in any desired orientation and projectors for sun, moon and planets separate from the star field projector and one another capable of projecting any possible orbit of the planets including those viewed from outside the ecliptic plane. Controlling and coordinating the drive means for the various projectors is a computer link which is preferably capable of being programmed for simulation of a selected view point in space for the planetarium audience, including a view point which is itself movable even as the planets are movable and which preferably is based upon an operational principal of vectorial summation.

United States Patent [72] lnventor Wallace E. Frank Westtown, Pa. [21App]. No. 549,831 [22] Filed May 13, 1966 [45] Patented Mar. 23, 1971[73] Assignee Planetaria, lnc.

Yorklyn, Del.

[54] SPACE TRANSIT SIMULATOR PLAllETARIUM 23'Claims, 34 Drawing Figs. 14 [52] US. Cl. 35/425- [51] Int. Cl. (20% 27/00 [50] Field of Search35/43, 45, 45.5, 42.5, 12; 88/24 (STAR), 24 (S); 235/189 (lNQUlRED) [56]References Cited UNITED STATES PATENTS 2,483,216 9/1949 Marshall88/24(STAR) 2,632,359 3/1953 Spitz 35/425 8/1957 Sargenti 35442.5

Primary Examiner-Jerome Schnall An0rneyl-lowson and Howson ABSTRACT: Aplanetarium capable of simulating planet, sun and moon movements andchanges as viewed from outside of, as well as within, cis-lunar space asprovided by a star field projector preferably capable of projecting aselected portion of the celestial sphere in any desired orientation andprojectors for sun, moon and planets separate from the star fieldprojector and one another capable of projecting any possible orbit ofthe planets including those viewed from outside the ecliptic plane.Controlling and coordinating the drive means for the various projectorsis a computer link which is preferably capable of being programmed forsimulation of a selected view point in space for the planetariumaudience, including a view point which is itself movable even as theplanets are movable and which preferably is based upon an operationalprincipal of vectorial summation.

PATENTED mas IHYI sum 05 HF 1Q .mw v4:

' mvcu'ronz WALLACE E. FRANK PAIENTEU BAR? 3 l9?! QNQE B WALLACE E.FRANK ATTYS,

SPACE TRANSIT SIMULATOR PLANETARIUM This invention relates toplanetariums and particularly to,a novel planetarium system which iscomputer controlled to a higher degree than in the prior art for greaterflexibility than prior art instruments. The system of the presentinvention provides greater flexibility in that it is capable ofsimulating observer position anywhere in the solar system and it islikewise capable of simulating to a higher degree than in the past theeffects seen in cis-lunar space,,the solar system regions close to theearth and moon. p

In my copending application Ser. No. 356,093, filed Mar. 31, 1964, nowUS. Pat. No. 3,256,619, a planetarium instrument is described in whichthe prior art limitations to clockwork coupling of planets to the starfield projector is eliminated, as far as the planet simulation aspectsof the equipment are concerned. The planet analogues of that system arecapable of selective repositioning in any selected part of their orbitposition. However, the analogue elements simulating the planets arelikewise limited to simulation of orbits as seen from earth or nearearth space. Heretofore, in fact, planetarium systems in general havebeen earth-bound in that all of the effects generated by the planetariuminstrument in the system are limited to those which would be observedfrom the earth or near the earth.

The present invention goes a major step further, permitting not onlyrelease from the time related limitations but also release from positionin space related limitations to the extent that any position in solarsystem space may be simulated. In accordance with the present inventionany place within solar system space can be simulated.

The function of the system of the present invention is to define thepositions of the sun and planets as seen from earth, from any planet, orfrom any general observer position within the general limits of thesolar system. The system is, therefore, capable of all effects of priorart systems in defining the positions of the sun, moon and planets asseen from earth. It is also capable of defining the positions ofthe-sun, moon and planets and earth as seen from other places within thesolar system.

In accordance with a related invention of Leonard Skolnick, this is doneby employing coordinate conversion computers to change polar orspherical observational coordinates to rectangular coordinates. Means isused to take the difference between the corresponding rectangularcoordinates to produce the components of line of sight vectors from aviewer position to a viewed point in celestial coordinates. (The inputto these computers is information about the position of a line of sightvector.) This information is then converted to room coordinates byposition computers to generate the signals necessary to position theprojector which simulates the viewed point. The concept of use of lineof sight computation in itself appears to be new and additionally theuse of the radial distance for any purpose in a planetarium is believedto be new.

Such information can be generated in a variety of ways, but thepreferred manner of doing so is by employing a reference frame such asone defined by a system having an origin at the center of the sun andaxes extending respectively toward Polaris. the vernal equinox and adirection mutually perpendicular to these two. According'to theinvention of Leonard Skolnick positions designated on the star sphere interms of latitude and longitude or other means, some of which will bedescribed herein, and radial distance from the sun as origin are thenconverted into terms of rectangular coordinates (e.g., x, y and z)mutually perpendicular to one another, and preferably one in whichPolaris supplies the z axis and the vernal equinox the x. Obtaining lineof sight vectors is a simple operation once the rectangular coordinatesare obtained. The concept of taking general information about viewedpoint position, referencing it with star field projector coordinates ina planetarium room and generating an output to direct a projector is anew approach, however.

For invention makes possible the use of an earth-centered referencesystem when considering cislunar space. This reference frame, is, inturn, capable of coordination within the sun-centered reference systemforother parts of the solar system through the earth simulation in thatsystem. (is-lunar space in this instance is defined to extend twice themoon's distance from earth. The relative positions of the earth. themoon and an observer at any selected location in cis-lunar space can bedefined by techniques similar to the techniques used for planets andgeneral observers in solar system space. The present inventionadditionally permits realistic simulation of the phases of the moon andof the earth from any observed position. It also permits correction ofthe view of the moon and of the earth in and near the orbital plane ofthe moon. It also permits correction of moon and earth attitude as anobserver changes position in cis-lunar space.

For a better understanding of the present invention, reference is madeto the following drawings, in which:

FIG. 1 shows a schematic sectional view of the planetarium including theplanetarium instrument, the domed auditorium and the console;

FIG. 2 is a side elevational view of the planetarium instrumentincluding separate planet and star field projectors;

FIG. 3 is a sectional view taken along lines 3-3 in FIG. 2;

FIG. 4 is a sectional view taken along lines 4-4 in FIG. 3;

FIG. 5 is a sectional view taken along lines 5-5 in FIG. 2;

FIG. 6 is a view similar to part'of FIG. 2 showing a modified celestialsphere projector;

FIG. 7 is a plan view from above along lines 7-7 in FIG. 2 of one of theplanet projectors;

FIG. 8 is a side elevational view of the planet projector structureshown in FIG. 7, partially broken away and shown in section;

FIG. 9 is a diagrammatic representation correlating a preferredcoordinate system employed to advantage in the practice of the presentinvention with the axes of the planetariuminstrument;

FIG. 10 is a schematic diagram showing the orbit and position of aplanet superimposed on the preferred rectangular coordinate system ofthe'present invention;

FIG. II is a schematic circuit diagram of a coordinate conversioncomputer for planet position;

FIG. 12 is a schematic diagram similar to that of FIG. 10 but specificto the orbit and position of the earth;

FIG. I3 is a schematic circuit diagram of a coordinate conversioncomputer for earth position;

FIG. 14 is a coordinate conversion computer for generalized observerposition in solar system space;

FIG. I5 is a schematic diagram of a system combining planet and earthcoordinate conversion computers into line of sight computers in an earthmode of operation. wherein the planet and the sun are observed as theywould be from the surface of the earth. expressed in the celestialreference frame;

FIG. 16 is a schematic diagram of a system combining general observerwith earth and planet coordinate conversion computers into line of sightcomputers in a general observer mode of operation, wherein the earth;another planet and the sun are observed as they would be from someselected position in solar system space;

FIG. 17 is a schematic diagram of a system for line of sight computersin a planetary mode of operation wherein the earth and another planetand the sun are observed as they would be from a third planet;

FIG. 18 is a schematic circuit diagram of a planet position computer; 7

FIG. 19 is a schematic circuit combining a general observer with a mooncoordinate conversion computer into a line of sight computer whereinthe-moon is observed as it would be from a selected position incis-lunar space;

FIG. 20 is a schematic circuit diagram of a coupling system for couplingcomponents permitting an earth-centered view into a sun-centeredcoordinate conversion and line of sight computer system;

FIG. 21 is a schematic diagram of the earth, sun and moon showing thegeometry of moon phasing;

FIG. 22 is a schematic circuit diagram of a system to compute moonphasing in the planetarium;

FIG 23 is a schematic diagram illustrating one means of solving theproblem involved in moon attitude control;

FIG. 24 is a schematic circuit diagram showing the computer system formoon attitude control;

FIG. 25 is a schematic diagram illustrating the geometry of moon viewcontrol;

FIG. 26 is a schematic circuit diagram of the moon view controlcomputer;

FlG. 27 is a composite schematic diagram of one embodiment of a completeplanetarium system in accordance with the present invention;

FIG. 28a is a schematic diagram representative of the spherical trianglewhich must be solved by computer to properly position the star fieldprojector of FIG. 2;

FIG. 28!) is a schematic diagram representative of the modifiedspherical triangle which must be solved by computer to properly positionthe star field projector of FIG. 6;

FIG. 29 is a block diagram showing computer components which may beemployed with the planetarium of the present invention;

FIG. 30 is a schematic diagram of a general daily rotation computer foruse with a star field projector;

H0. 31 is a schematic diagram of acomputer which compensates for a shiftfrom a vertical to a nonvertical axis in a star field projector;

FIG. 32 is a schematic diagram of a computer which compensates for ashift in a polar axis of'a star field projector from a positionextending through Polaris; and

FIG. 33 is a schematic diagram of a computer which superimposes aselected amount of pitch. roll and yaw move ment upon the position ormovement of a star field projector.

Referring first to FIG. I. an installation in a planetarium similar tothat disclosed in my US Pat. No. 3,256.6l9 but differing in theinstrument employed is shown. Typically, this installation will consistof the planetarium instrument 1 centered in the room, a hemisphericaldome 2 positioned above the room with the instrument arrangedapproximately at its center. Suitable seating is preferably arrangedwithin the room along a floor which is stepped as shown. butalternatively may be of conventional circular arrangement on a flatfloor. A control console 3 is located somewhere in the room. preferablyin the back in a situation where auditorium seating is employed. Fromthis console. the planetarium show is set up and programmed and the modeof operation of the planetarium as well as special effects may becontrolled. The console will include instrument controls, meters. inputselection switches and other equipment, but much of the controlequipment need not be in the console or the instrument but may be storedin a side room or elsewhere out of the way and connected to the consoleand instrument by suitable cable or other links in conventional manner.

As seen in FIG. 2 the star field projector 4 of the planetariuminstrument 1 is preferably separate from the projectors which projectcelestial bodies other than the stars. such as planets, the sun. themoon, the earth, and natural and artificial satellites of all types. Thepresent invention by permitting separation of the planet and auxiliaryprojector from the star field projector makes it possible to greatlyreduce the mass and possibly the volume of the star field projector sothat its moment of inertia may be drastically reduced. The low inertiaenables the use of auxiliary effects such as roll. pitch and yawsimulation. The separate projectors for each planet are also low inertiatypes and highly flexible in operation. Being separate these projectorsrequire continual computer controlled coordination with the star field.The planet movements must be capable not only of being superimposed onthe diurnal motion and other motions previously associated with thechanging of a viewer position on the earth's surface but any motionsimulating changes in viewer position and orientation in space. Separateprojectors capable of universal positioning also permits planets, sun,moon and earth projections against any portion of the star field. notjust the general area of the ecliptic. thus permitting simulation ofview of their orbits from any possible vantage point. This addedflexibility, is. therefore.

important in simulating space ship flight. or the like. and simulationof effects of roll. pitch and yaw may make such simulated flights seemeven more realistic.

STAR FIELD PROJECTOR CONSTR UCTlON Referring in particular to the starfield projector 4 of FIG. 2 and the associated FIGS. 3. 4 and 5. manydifferences between this projector and those of the prior art arereadily apparent. ln the same respects the present projector differsfrom the intermediate space travel planetarium of my copendingapplication Ser. No. 356.093. Most apparent is the separation of thestar field projector 4 from the planet projectors 5 so that the starfield projector may be consolidated into a spherical unit or hollowspherical shell 10. The shell 10 contains a suitable light sourceassociated with suitable horizon defining cutoff means and will beprovided with conventional appropriate lenses and pinholes to simulatethe brighter stars and galaxies in the celestial sphere. Only anapproximate hemisphere will be projected onto the planetarium dome atany one time. however. In order to permit this star field projector tosimulate the heavens as seen from any place on earth or any location insolar system space. the sphere [0 must have the capability of allpossible rotational orientations about its own center relative to theplanetarium dome 2 in the arrangement shown in HO. 1. In order toaccomplish such reorientation. the sphere is provided with at leastthree axes of rotation designated. respectively I. ll. lll. In a threeaxis system axis l is preferably a polar axis arranged to coincide withthe polar axis ofthe earth for convenience in simulating earthboundeffects such as diurnal rotation which takes place about its axis. Axislll is preferably a vertical axis about which sphere 10 is rotated inorder to change the heading relative to the planetarium dome. Axis ll isnormal to axis l and lll and in the preferred embodiment is used tosimulate differences in declination. Axes l and lll may. ofcourse. beotherwise oriented.

As seen in FIG. 2. Axis lll is provided by yoke structure H whichrotates on bearings between its vertically oriented stem 12 and asuitable sturdy support base l3. which. in turn, may be fixed to thecommon pedestal l4 shared with the planet projectors 5. A motor 15 fixedto the base is used to drive shaft 12 rotationally relative to the base13 about the generally vertical axis lll as result of engagement of therespective gear 16 fixed to the motor shaft and stem 12. Similar gearconnection couples a resolver 17. or similar position sensor. to shaft[2 to sense the angular position of shaft 12 about axis lll relative toa predetermined reference. The arms l8 of the yoke 11 provide thebearings for trunnionlike projections from ring 20 which are alignedwith and define axis II. A motor drive 2| is supported on one ofthe yokearms l8. (see FIG. 5 A gear 22 on the shaft of motor 21 drives gear 23on one ofthe trunnions l9 and. therefore. the ring 20. to which thetrunnions are fixed. relative to yoke arms 18 about the horizontal axisll. As seen in FIG. 5 a resolver 24 is employed for sensing therotational orientation of the star field projector about axis ll astaught in my copending application Ser. No. 356.093. Resolver 24 issupported on yoke 18 with its shaft fixed to rotate with trunnion l9.

The sphere 10 is. in turn. rotatably supported on the ring member 20 insuitable bearing means by aligned. rodlike projections 27. which defineaxis l and one of which provides the shaft of resolver 28 fixed to thesphere 10. In the embodiment shown movement of the sphere 10 relative toring 20 about axis l. preferably the axis of Polaris. is producedthrough the equatorial ring flange 29 on the sphere 10. As seen in FIGS.3 and 4. flange 29 is engaged by a pair of rollers 30. beveled edges ofwhich are urged against the beveled edge of the periphery of the ringflange 29 to provide a frictional contact such that, when one of therollers 30 is rotationally driven. the flange 29 is frictionally movedby the rollers. thereby driving the sphere 10 about its axis l definedby projections 27. The rollers are supported within p: rallel flanges ofa bracket 32 supported. in turn. by ring 20. as best seen in H6. 3. Therolllll033 0392 lers are provided with aligned shafts 33 journaled inbearings in the parallel flanges 34 of the bracket 32 and are springurged toward one another along their shafts by spring elements 35. Ringflange 29 is trapped between the rollers 30. One of the roller shafts 33is terminated in a bevel gear 38 which, in turn, engages a bevel gear 39ona shaft 40 journaled in a part of the same supporting bracket 32, towhich bracket the motor 421s also afi'rxed. The shaft 40 is preferablythe shaft of the motor 42 so that drive by the motor is transmittedthrough the bevel gear 40 to bevel gear 38 and hence roller 30 on shaft33. Because of the spring urging into frictional contact with the ringflange 29; both rollers 30 travel at thesam speed and therebydriv'eflangei29and the sphere l0.

Because of certain problems resulting from gimbal-lock in order to givethe star field-projector, great'er'flexibility, it may be provided witha fourth axisas seen in the structure of P16. 6. This arrangement makesit possible for the polar axis to pass through zenith orientationswithout 180 shifts about one or more of the axes and without responseproblems which occur frequently'in connection with a three axesarrangement. Referring to FIG. 6, corresponding parts are givencorresponding numbers with the addition thereto of primes. In this case,instead of vertical shaft 50 serving as the stem of the yoke ll shaft 50is instead affixed to an arcuate segment shaped supporting member 52,which, in turn, rotatably'supports the stem 12' of the yoke II" in asuitable bearing arrangement permitting rotationabout" the axis of stem12'. A drive motor 54 supported by the base 13" through'gears 55 drivesshaft 50 thereby driving the segment member 52 to establish the headingof axis I ll defined by shaft 12'. Segment member 52 itself is drivenrotationally relative to the base 13' about the axis of itsvertically'oriented shaft 50. A syncho or resolver type pick up 56sensed the, position of shaft 50 and segment 52. Stem 12" may stillbeconsidered axis lll titled by an angle T. The yoke 11" is driven bymotor through shaft 12' by means of gears 16. Synchro or resolver l7senses shaft position about axis lljl. Gear 17' is coaxially fixed .toshaft 50.'lt will be observed that shaft 50 provides a new fourth axisand that'relative rotation is possible about all four axes.

Except for the differences in form-cited; it may be presumed that thestar field projector 4 of FIGS. 2 through 5 and that of FIG; 6 are inall essential respects 'similar to one another and except fordifferences recited and obvious from the drawings the star fieldprojector, its rotational abilities, and associated structure forproducing and sensing relative rotations are similar to those describedin my copending application Ser. No. 356,093.

. PLANET PROJECTOR CONSTRUGTION Associated with the star field projectorare a plurality of planet projectors which may be varied in numberinaccordance with the desired display. The term planet projector" asused herein will be understood to include moon, sun, earth and naturaland artificial satellite projectors. To schematically represent onepossible arrangement, a number of planet projectors are shown in FIG. 1having differing heights so that they will not occlude one another andto minimize occultation of light from the star field projector and sothat the star field projectorwill riot occlude light fromthem. Variousalternative arrangements can be used to this end with the planetprojectors even widely separated and located at the edges of the room.If the star field projector is centered, then corrections for theoffcenter positions of the planet projectors have to be madeto obtainproper orbits of their respective planets. Such correction can be madein the signal fed to the motors of the planet projectors. The individualplanet projectors are supported upon their trestles above the base 14.The base 14 may be of any suitable form or may be omitted. The trestles60may beof any suitable form. Associated with each of the planetprojectors is a light source6l whichis provided to simulate theparticular celestial objects being projected in terms of size, color,features andorientation; The light source is preferably arranged toproject its beam upwardly through the top of the trestle 60 to impinge amirror 63. Mirror 63 preferably has a fixed angle relative to the beam,preferably on the order of 45 to the vertical, which reflects the lightfront a vertical into a horizontal beam path. The light beam, in turn,is reflected from the horizontal by a second mirror 65 which reflectsthe beam into the properdirection to impinge the planetarium dome 2 at aselected place.

A better understanding of the mirror system of the planet projectors maybe had by reference to FIGS. 7 and 8. Referring particularly to FIGS. 7and 8, it will be seen that the mir rors 63 and 65 are mounted on aturntable 67 atop the trestle 60. The turntable has a verticallyoriented axis and is provided with'suitable bearings betweenthe top ofthe trestle and the turntable. Rotation of the turntable relative to thetrestle is accomplished by means of the motori-68 fixed to the trestlewhose shaft drives turntable 67 which through gears 69 also drivesynchro or resolver 70. Fixed to the turntable to rotate with it isbracket 72' supporting mirror 63 in its selected position, eg atapproximately 45 to the vertical light beam. The turntable and relatedstructure ispreferably hollow so that the light beam from light source6| may pass through it and impinge mirror 63 without occlusion. Mirror65 is rotatably supported on the turntable bracket portion 74' by ashaft 75, generally aligned with the light beam, which is reflected fromsource 61 by mirror'73. Shaft 75 is'journaled in the bracket 74 torotated about the longitudinal axis of the shaft 75 and the mirror 65 isattached fixedly to the end of shaft 75 preferably so that the plane ofthe mirror 65 makes a selected angle, here on the order of 45 with theshaft. Theanglcs are selected such that by the combination of rotationof. turntable 67 and shaft 75 the mirror 65 is capable of projecting thelight beam onto the zenith and every other point of the planetarium dome2. it this condition is satisfied'then by a combination of rotation ofthe turntable 67 and rotation of the shaft 75 the light beam can bedirected sequentially to all successive selected points in the planetorbit on the planetarium dome 2. Movement of the shaft 75 in arotational manner'is sensed by resolver 77 driven by gears 78 which alsoconnect motor 79 to shaft 75. Motor 79 and synchro 77 are also fixed tothe bracket 74. With a three axis star field projector system it ispreferable that the axis of the planet projector which is fixed in theroom be parallel to axis III of the star field projector.

Since the star field remains essentially unchanged within the solarsystem or at least within the range of the planets'visiblc with thenaked eye, star field projectors which do not change star positionsrelative to one another are quite acceptable, provided, of course, thestar field may be moved as a whole. However, the same thing is obviouslynot true of planets. In accordance with the present invention, theplanets are simulated in the planetarium by projectors which may bemechanically simpler than prior art planet projectors but which areresponsive to a novel system quite different from any system of theprior art. In accordance with this system, planets may be made to followpaths relative to the planetarium dome simulating what is seen by anearth-bound observer or equally well may be made to follow entirelydifferent paths on the dome simulating what is seen by an observerelsewhere in solar system space within the range of planets visible fromearth with the naked eye. The advantage of planet projectors built asanalogues of planet orbits as seen from earth is, therefore, lost exceptinthe earth mode of operation. Consequently, planet projectors of thepresent invention are preferably of extremely simplc constructionwiththe criteria that they must be able to simulate theplanet positionanywhere in'the planetarium dome with a movement which is smooth and ofa speed commensurate with relative speeds 'of other movement of theoverall planetarium system. The planet projectors, in short, must becapable of being driven by the associated computer to any requiredposition to simulate both the instantaneous position and orbit of theplanet. The projectors must, of course, be

coordinated with the star field projector since the planet orbits arewith reference to the star field. However, this reference may beprogrammed into the overall control computer.

7 PLANETARIUM REFERENCE FRAME In accordance with the present invention,it is necessary to select a universal frame of reference useful throughout solar system space. Most conveniently such a frame of reference issun-centered since the sun is the center of the solar system and theplanets revolve about it. It is possible to select in any manner asystem of reference axes for the star field, but, because ourearth-bound point of view will still occupy a large part of planetariumtime, a most convenient reference system is obtained using the directionto polaris as the z axis. The direction to the vernal equinox is then atright angles to this axis and, therefore, provides a convenient x axis.The third or y axis may then be taken mutually perpendicular to thesetwo. These axes are shown in FIG. 9 combined with the axes of theplanetarium equipment. Moreover, with polaris and the vernal equinoxselected as one pair of mutually perpendicular axes, the third axis willlie in the equatorial plane. In an earth-bound mode of the planetarium,this reference frame rotates with respect to the room about the polaraxis to simulate daily motion of the earth. Anywhere in solar systemspace simulated the reference coordinates are always identifiable andfixed relative to the star field. FIG. 9 also shows the ecliptic planesince it holds great significance in planetarium geometry.

The coordinate system developed in FIG. 9 is used in FIG. I to describea planet's orbit. It will be observed in FIG. 10 that the orbit of eachplanet defines a plane which intersects the equatorial plane at an angle(1 with the vernal equinox, which angle is constant for a given planet.The angle i between the planes is also constant. The position of theplanet, does, of course, vary within its orbital plane. If the planetsorbit is noncircular, r representing its radius or distance from the sunmay not be constant. The angular velocity 0) equals dig/d1 of the planetmay also be considered a variable with negligible error for purposes ofthis planetarium system. The angular position from some reference suchas the intersection of the orbital plane with the equatorial plane thenbecomes the only variable measured at the sun origin. The variable maybe generated in an analogue fashion, for example, by use of a commonvariable speed motor geared to produce the proper relative periodsrepresentative of revolution about the sun of shafts and otherassociated analogue devices representative of the planets, includingearth. The angular shaft position of the respective analogue meansrepresenting the planet then becomes the variable of the planetanalogue.

POSITION COMPUTERS It will be seen from FIG. 10, that from coordinateswhich correspond to right ascension and declination in the star fieldwith the radius r,,,,, added, at a given point in its orbit the planetposition may be expressed in rectangular coordinates of the planet x,,,y,,, and z,,, as shown in FIG. 10. Position location relative to thestar field is therefore in combination with use of the radius tocomplete the spherical coordinates. In accordance with the presentinvention, using position in the star field and radius information,rectangular coordinates are generated by coordinate conversioncomputers.

Planet position in rectangular coordinates in the sun-centered referenceframe of FIG. 10 is generated by the system of FIG. 11. In this system,three resolvers 80, 82 and 84 are employed. In this embodiment, theresolver 80 has a fixed signal input, which may be a signal relative toa standard and stored in a control computer for use at this input torepresent the radius from the sun origin of a selected planet. The inputalso may be set at a fixed level relative to inputs for other planets torepresent the constant average radius form the sun of a specific planetin the solar system. r may alternatively be made a function of g and 5need not be a linear function of time. This signal input r,,., to theresolver 80 induces a voltage in each of its mutually perpendicularcoils mounted on and rotatable by its shaft. In resolver 80 shaftposition is changed in response to the changes in angle which as seen inFIG. varies as planet position varies in the course of its orbit aroundthe sun. The outputs of the resolver 80 then, as shown, are r sin 5,which is fed to the input of resolver 82, and r cos 5, which is fed toone of two inputs of resolver 84 (dropping subscript of r,,,,,). Theshaft of resolver 82 which carries mutually perpendicular coils is fixedin position to represent the constant angle i between the plane of theorbit of the planet and the equatorial plane. As a result, the outputsof this resolver 82 are r sin 5 cos i, which is fed to the second inputof resolver 84, and r sin 5 sin 1', which, by trigonometric conversionis equal to the z,, rectangular coordinate. The shaft or resolver 84positions its mutually perpendicular coils to represent the angle 0.,which as seen in FIG. I0 is the angle of offset in the equatorial planeof the intersection of the orbital plane of the planet from the vernalequinox. Resolver 84 generates output signals r sin 6 cos i sin (I and'r sin 6 cos 1' cos I), which are respectively representative of therectangular coordinates .t',,, 2,.. As previously mentioned, in settingup the angle 5, the information normally available is EH). This is theinformation normally available from observational data and involvessufficiently small errors to be acceptable as an input in place of Ealone.

The diagram of FIG. I2 represents the orbit of the planet Earth, aspecial simple case of the diagram of FIG. l0. Specifically, in thiscase the angle (1 equals zero since, by definition, the vernal equinoxis the line of intersection of the equatorial plane and the eclipticplane, and by definition the ecliptic plane is the plane of the earthsorbit around the sun for our epoch. The distance of the earth from thesun r is one astronomical unit and serves as the reference for relativedistances of other planets from the sun, and i in this case is fixed at23%".

The simplified coordinate conversion computer for the earth is shown inFIG. I3. Only two resolvers are necessary because of the elimination of(I. A steady input signal to resolver representative of one astronomicalunit and a shaft position representing 5 produces outputs a sin 6 and ucos 5, the latter being the rectangular coordinate x... Resolver 82receives an input representative of r=23% and the output of resolver 82'represents a sin cos 2399 and a sin 6 sin 23% which respectivelyrepresents y,. and 2.. rectangular coordinates of the earth. Eclipticcoordinates, with a sun origin with x and y axes in the ecliptic planeand the z axis mutually perpendicular thereto, can even more easily begenerated for the earth. The ye coordinate is equal to a sin 6 which, aswill be observed, is the output of the resolver 80'. The x,. coordinateremains a cos 5, and, of course, for earth 2,. is zero. Eclipticcoordinates for planets having orbits out of the ecliptic plane will. ofcourse, have a z coordinate which may be generated using the eclipticplane instead of the equatorial plane as the reference.

A generalized observer position, may be obtained by the observercoordinate conversion computer of FIG. l4. It should be borne in mindthat in solar system space, astronomical measurement may be in eitherecliptic coordinates or in equatorial coordinates. Assuming that x theobserver would reference his position in ecliptic coordinates and thatobserver latitude is d1 observer longitude is 9 and observer distancefrom the sun is r,,.,., then the input to resolver 86 is an input signalproportional to r,,,,. The shaft position of resolver 86 isrepresentative of observer latitude. Therefore, resolver 86 produces anoutput r,,,, sin 11: which is fed as the input signal into resolver 86.Resolver 86 also produces an output r,,.,, cos ill which represents ZThe shaft position of resolver 86 so that its outputs represent observerlongitude 1 are r,,,, sin ll! sin I and r,,., sin r11 cos D,respectively. representing y and x Coordinate representative signals y,,and 2 respectively are fed into resolver 90, whose shaft position isrepresentative of the ecliptic angle of 239?. The output signals ofresolver 90 are equatorial rectangular coordinates equal to z,, and y,,,the

equatorial coordinates of the observer. The x, output of resolver 86 isalso by definition x without further modification.

9 LINE OF stoi-ir'aiMpuroas FIGS. 15, 16 and 17 are schematics showingrepresentative combinations of coordinate conversion computers of FIGS.11, 13 and 14 into line of sight computers for computing the directionfrom a selected viewed point. Either or both of the viewing position andthe viewed point may be changing position as is contemplated by thevariable inputs in the coordinate conversion computers of FIGS. 11, 13and 14. The ex amples of FIGS. 15, 16 and 17 are intended to berepresentative and in no way limiting as to possible combinations.

FIG. shows one means of computing line of sight vectors from the earthto a representative planet. The information derived could be used todirect the projector for that planet through its successive orbitalpositions relative to the star field as viewed from earth. It will beunderstood that ina practical planetarium system each planet coordinateconversion computer may be tied into the earth coordinate conversioncomputer in the same way to provide a line of sight direction of theassociated planet projector to simulate the view from earth. In thissystem, the planet coordinate conversion computer 92, which wasillustrated in FIG. 11 and described in connection therewith, iscombined with the earth coordinate conversion computer 94 which wasdescribed in FIG. 13 and described in connection therewith. Morespecifically, the respective coordinate output signals of each computerare combined. By selective connection of the output terminals from earthcoordinate conversion computer, output signals x,., y,. and 2,. may beselected as either positive or negative signals. Negative signals x,.,y,. and -z, are, respectively, equal to the sun coordinates +x,,, +y,and +2, defining a line of sight vector from earth to sun. The x signalsfrom planet coordinate conversion computer 92 and earth coordinateconversion computer 94 are summed in summing amplifier 92x.Corresponding y and 1 signal outputs are summed in summing amplifiers98y and 98z. Since outputs from computer 94 are negative, the summingamplifiers 98x, 98y and 981 produce difference output signals, whichtaken together define the line of sight direction from earth to theviewed point. These signals fed into an appropriate planet positioncomputer produce appropriate heading signals to direct the planetprojector, such as the ones shown in FIG. 2, 7 and 8. The negative earthcoordinate signals from the earth coordinate conversion computerrepresent without further change sun coordinate signals in asun-centered coordinate system wherein the sun is at the origin fromwhich the planet position coordinates are measured. That is, since thedistances are the same but the direction is opposite, the negativeof theplanet coordinates define the direction to the sun. These negative earthcoordinates are, therefore, used to position the sun projector. Mean suncoordinate position can be generated in a similar way by coordinateconversion computer 94 usirlg negative ecliptic coordinate outputs -Xeand -Y,.'*', respectively, It will be appreciated that in this, as .inany mode of operation, there are other planet coordinate conversioncomputers for each of the planets simulated. A single earth coordinateconversion computer used as viewer positionis used with every planetcoordinate conversion computer in exactly the same manner to define thevector direction from earth to that planet for each of them.

In the general observer mode, the earth becomes merely another planet.Thus, the general observer line of sight computer of FIG. 16 employs aseparate observer coordinate conversion computer 94' corresponding toearth coordinate conversion computer 94in FIG. 15. The numberscorresponding to those designating the corresponding parts in the earthviewer line of sight computer of FIG. 15 are given corresponding primednumbers in the general observer line of sight computer of FIG. 16,designating the similarity of the roles. The observer coordinateconversion computer 94 is analogous in its role to the earth coordinateconversion computer 94 .of

FIG. 15 and its negative output signals are selected for use in the samemanner. The negative signals thus derived are com ponents of the line ofsight vector to the sun as viewed from the observer position. Thesesignals are combined with signals representing corresponding componentsfrom the planet coor dinate conversion computers at summing means 98x,98y, and 98z' to derive the component signals representing the line ofsight vector from observer position to the vicwed point in terms ofrectangular coordinates. The earth coordinate conversion computer 92,.is the same in type as those for any other planet and earth line ofsight components are derived through summing means 102x, 102y and 1022,.The mean sun position coordinates are derived by selecting the negativeoutput of the ecliptic coordinates generated at coordinate conversioncomputer 94. In this instance, three ecliptic coordinate signals arerequired since observer position can I theoretically by anywhere inspace.

Planetary mode of operation is illustrated in FIG. 17 wherein theobserver is selected to be on any planet other than earth and the planetand earth coordinate conversion computers 92 and 92,. provide the samefunctions they assumed in the general observer mode of FIG. 16; Insteadof a general observer, the observer's viewing position is another planetwhose changing coordinates are generated by coordinate conversioncomputer 94". Negative signals are selected in the same way fromobserver coordinate conversion computer 94 and added'in the same way bysumming means 98x", 98y" and 98z" and 102y', 102x and I02z'.respectively.

Posmon COMPUTERS Referring now to FIG. 18, a typical position computersystem is schematically illustrated. These position computers can beused to direct'the projector for projecting the image of the planets,earth, moon, sun or any natural or artificial satellite. It will beappreciated that this same computer can be used as a sun positioncomputer. earth position computer and the like, its function being totake the different signals representing the rectangular coordinatecomponents of the line of sight vector of the viewed point in each casein the celestial reference frame and by a suitable computation obtainline of sight azimuth and elevation signals in the room reference frameto be used to drive a suitable planet projector. In the systemillustrated in FIG. 18 a general planet position is derived and thesignals x,,-x,, and y,,y, (where the subscript p refers to the planetand the subscript a to the observer) are fed into resolver whose shaftposition is representative of the angular position 1 of the polar axis(axis 1) of the planetarium instrument. The output of this resolver yand .r', the respective components of the line of sight along the normalto the horizontal axis (axis 11) in an equatorial plane y and z,rz.,.are fed into the second resolver 112, whose shaft position isrepresentative of 90 1 (the colatitudc of the planetarium .instrument).The output of resolver 112 is respectively y". 1" which are thecomponents of the line of sight vector normal to and in the x axisdirection along the planetarium horizon plane and along the zenith,respectively. The y" signal and the .r" signal are fed into resolver114, whose shaft position is the planetarium azimuth positioned byvertical axis 111. The output of resolver 1-14 is, respectively, x' andy, components of the line of sight vector along the polar and horizontalaxes of the planetarium instrument.

In the preferred embodiment where axis 111 is vertical. the outputs ofthe resolver 114 are both fed as inputs to resolver 116 whose shaftposition fixes the planet's elevation. The outputs from resolver 116include an output through a signal amplifier 118 to a motor 120 whichdrives the elevation position shaft in the event that elevation positionis not correct. This signal continues and the motor continues to driveuntil no signal is received at the appropriate output of the resolver.

The other output of resolver 116 is used as an input to a modified shaftposition determines the coil positions in resolver 122. The signal willbe generated through signal amplifier 124 until the motor is in correctposition to null out any signal, at which point the correct azimuth willbe achieved. In the event that axis III is not vertical the position ofthe planet will still be correctly fixed by the above computationprovided the fixed planet projector axis is parallel to axis Ill, but inthis case the outputs will not correspond to azimuth and elevation ofthe planet.

CIS-LUNAR MODE When operating near the earth or the moon, one must takeinto consideration some of the errors that otherwise can be neglected insun-centered operation. Moreover, in operating close to the earth, it ismost convenient for the sake of simplicity of computation to operate inan earth-centered mode rather than using some other cis-lunar center.This earth centered mode can, if necessary, be keyed into sun-centeredoperation of the rest of the planetary system.

The problems peculiar to the earth and moon generally occur within aradius from earth of about twice the distance from the earth to themoon. In this portion of solar system space in addition to the problemsof positioning the moon and the earth in the planetarium, it isnecessary that both bodies be properly phased, have the correct attitudein the celestial sphere and be viewed from the proper side and haveproper size. The output voltage from the earth and moon positioncomputers is proportional to the distance between the observer and thecelestial object and can be used to control the size of the projectedimage on the dome. Each of the other problems is related and yetrequires separate solution and separate computer means. Since in mostcases the problems having to do with viewing the earth are analogous tothose viewing the moon, a consideration of the disposition of theproblem with respect to the moon can be transposed by those skilled inthe art to the analogous problem of the earth. Accordingly, the problemswith the moon will be specifically considered and be understood to applywith equal force to the corresponding problem with regard to the earth.

As suggested above. moon position in the solar system when near theearth, must be considered for the sake of accuracy in representingrelative moon and earth relationships. Therefore, an earth-centeredcoordinate frame is essential in considering moon position withincis-lunar space. In considering the -problem in earth-centered insteadof sun-centered coordinates, the diagram of FIG. is analogous to onewhich might be drawn for the earth-centered coordinates. Since this isso, it will be apparent that the coordinate conversion computer for moonposition in an earth-centered system shown in FIG. 19 is quite analogousto the computer of FIG. II for a planet in a sun-centered system. Onedifference which must be taken into consideration in the earth-centeredsystem is that, instead of having the orbit maintain a fixed positionwith respect to the frame of reference, the ascending node of the moontends to shift. That is, the angle 0 is variable since the longitude ofmoonrise or the ascending node of the moon's orbit is variable. Also,the moon data is normally obtained in terms of ecliptic plane referencerather than equatorial plane and, in order to take advantageconveniently of the tabulated data, the reference should be readilyavailable in the ecliptic plane rather than the equatorial plane. Inorder to obtain a line of sight vector with accuracy, it is, therefore,necessary to obtain the observer's longitude and latitude expressed inecliptic coordinates. This is done with respect to the earth rather thanthe sun for the reason mentioned above.

Referring to FIG. 19 the moon coordinate conversion computer and anobserver coordinate conversion computer have been combined in a line ofsight computer to generate coordinates of the line of sight vectorwhenever required. The moon coordinate conversion computer consists ofthe resolver I40, I42, and 144 with inputs and outputs and appropriatecoupling as shown. An input signal proportional to the radius from thecenter of the earth to the center of the moon is provided to resolverwhose shaft is angularly positioned to represent the moon's positionangle which corresponds with f in FIG. 10 but is here represented asacrescent (I. Actually because tabulated date is normally not availablein that form, the input usually is O, which may be expressed as w. Sincethe longitude of the ascending node shifts, II is no longer fixed aswith planets, but is a variable and mechanically suitable differentialmeans must be provided to accept (I and (I inputs in order to obtain anaccurate (I --(1 input at the shaft. The out put r,..,,, sin ((-0) isfed to the resolver I42 as its input. The shaft position for resolverI42 is the angle 1', about 5V4, between the moons orbital plane andecliptic plane. The cos output of this resolver is x,,,'-'. The sinecomponent r,.,,,. sin 1' sin (([(I) I42 provides one input to resolverI44. A second input to resolver 144 is the output a signal r,,,,,, cos(-11) of resolver I40. The shaft position of resolver 144 isrepresentative of (I, the angle between the vernal equinox and theascending node of the moons orbit. Since .(I, is variable in thisinstance, suitable means to generate the variable signal is provided toposition the shaft. The output of resolver I44 at the sine output is 1and at the cos output is y,,.". Since the outputs from the mooncoordinate conversion computer are in terms of moon position as viewedfrom an earth centered system, in order to obtain observer line of sightdirection, observer position must be known in the same system ofcoordinates. Moreover, rectangular coordinates must be obtained and thisis done by means of resolvers I46 and 148. A signal proportional to theobserver radius from the center of the earth r is the sole signal inputof resolver I46, whose shaft position is representative of observerlatitude sla The cosine output of resolver I46 is directlyrepresentative of the Z coordinatc z.,,-. The output r sin ll) ofresolver I46 is fed as the sole input to resolver I48. The outputs ofresolver I48 represent the rectangular coordinates x,,,.. which likeoutput 1 may be selected as negative signals by lead reversal. Thecoordinate signals are summed by summing amplifiers l50.t. l50y and I50zto give output differences of the signals x,,, x,,,.' y,,,"'y,,,."" andz,,,z,,,. which represent respectively the moon vector coordinates inthe ecliptic system as viewed from earth, x,,,,,"", y and z,,,,.. Theshaft position of resolver I54 is representative of ecliptic anglei=23'vz. Coordinates are transferred from the resulting ecliptic line ofsight rectangular coordinate components to such coordinates withreference to the equatorial plane y and 2 by putting signals intoresolver I54. Coordinate x,,,,, by definition is the same as coordinateThe moon coordinate computer and line of sight computer can be used withappropriate different inputs to the rcsolvcrs I40 and 144 to simulateany earth satellite. This can be done using the same computer of FIG. l9supplied for the moon or by supplying additional computer components, ifartificial earth satellites are sutficiently important in a givenplanetarium installation.

In many planetariums, it will not be necessary to provide couplingbetween the earth-centered observer reference frame and the sun-centeredreference frame. In such event, it will be understood that the moonposition computer corresponds exactly to the planet position computer ofFIG. I7. However, coupling earth and sun centered systems together canbe accomplished as shown in FIG. 20, should this be necessary ordesirable.

FIG. 20 shows the means of transferring from the earth centered observerframe to the sun-centered frame or tying the two reference framestogether. Since the earth has no elevation, its azimuth with respect tothe sun is all that is necessary to be fed in as a shaft position toresolver I60. Resolver receives an input signal representing a, oneastronomical unit (the distance between the earth and the sun). Theoutput of resolver 160 is earth position in terms of ecliptic x and ycoordinates. By contrast, general observer position in cislunar spacerequires more input information. Observer latitude th fed into resolverI62 as a shaft position to effect a signal proportional to the radiusbetween the earth and the observer. The r,,,. sin 111,, output ofresolver 162 is fed into resolver 164 and the cosine coordinate directlyrepresents the component ZNE. The shaft position of resolver 164 isrepresentative of observer longitude b relative to the earth so that theoutputs of resolver 164 are x and y coordinates of the observer in theearth-centered system, still in an ecliptic reference frame. The x and yobserver coordinates relative to earth are selected to be negative andcombined with the earth position coordinated relative to the sun at thesumming amplifies 166x and l66y, respectively. The output signals x-xfi,and -;g, are supplied to resolver 168 as input signals; The" shaft ofthis resolvenrepresents observer longitude in a sun centered system andits sine output winding produces a signal which is amplified in signalamplifier 170 and fed to motor 172 which drives the shaft of resolver168 until the signal generated by the resolver sine coil is nulled out.This shaft position then represents the proper position of the observerlongitude in a sun centered system. Since resolver 174 in anobserver-sun computer has a common shaft with resolver 168 and motor172, the shaft of resolver 174 also represents an observer longitude.The cosine output of resolver 168 is then fed to resolver 176 which alsoreceives the cosine signal output of resolver 162 which represents 1...?These two signals are combined by resolver 176 whose shaft position isrepresentative of observer latitude i11 relative to the sun. The sinecomponent of the signal is used to connect the shaft position ofresolver 176 which is representative of the observers sun latitude. Thesine signal output from the resolver 176 is fed to amplifier 178. If theshaft position of resolver 174 representing observer latitude th iswrong, a signal is generated which drives motor 180 to reposition theshaft until no signaloutput is obtained, at which pointlthe latituderepresented by the shaft is proper. The same shaft position determinesthe position of the shaft of resolver 182 in the observer-sun system.The other output of resolver 176, the cos component, is a signalrepresentative of the radial distance of the observer from the sun andcan therefore be fed directly into the resolver 182 as its input signal.The sine output of resolver 182 provides an input for resolver 174 andthe cosine signal provides an x observer coordinate. The y and zobserver coordinates, are, in turn, generated by the output of resolver174, whose shaft position is determined by motor 174 and represents thelongitude of the observer position in thesun system. This observeroutput is the same asthe general observer output in FIG. 14.

The problem of moon phasing is diagrammed in FIG. 21. This becomes aplane geometry problem in the sense that the earth, the moon and the sunmay be considered to be in an essentially common plane. Taking thevernal equinox as the reference direction from earth, the angle of thesun 1 relative to the vernal equinox as viewed from earth is one valueof importance. The angle (1 representing the angle between the moonandthe vernal equinox as viewed from earth, is another value ofimportance. IL- 1: is the information required to operated a moonphasing control of known type. This phasing control will be operated onthe principle that when l is equal to zero, the moon cannot be seen fromearth, since only the moons side away from earth islit. When I Q equals1r radians, the side of themoon towardearth is fully lit and the moon isfull. Intermediate phasing of the mooncan then be .calibrated asdifferent positions between these two output signals from the earthanalogue representing the coordinates x, and y, in the ecliptic systemand in the plane of the ecliptic. As shown in FIG. 22 these signals arefed to the moon phasing resolver 184 which has its shaft positioned torepresent angle Q at resolver 184. Both sine and cosine component signaloutputs of the'resolver are fed as inputs into resolver 186. The shaftof resolver 186 is positioned to .represent D -Q The sine output ofresolver '186 is amplified Rby signal amplifier 188 and fed to motor 190which drives the shaft until it reaches the position where no signal isgenerated and, therefore, is properposition to represent (P -K Thisshaft, in turn, is coupled to the phasing mechanism for the moon.

As previously mentioned, a similar phasing device can be provided forthe earth. In the computation of the moon phasing, the component of themoons orbit which does not lie in the ecliptic plane is neglected andmakes no substantial difference in the effect.

The moon attitude control has to do with the heading of the pole of themoon with respect to the viewer. In actuality, the polar axis of themoon points approximately to the ecliptic P v xen i l snlsnet riv is ares vn q p mation, and greatly simplifies the problem, if the assumptionis made that the moons pole points instead toward Polaris. This enablesthe axis of the moon to point along its local meridian, i.e., the pointpassing through the zenith M or deviate therefrom by simple manipulationof the projector axis. FIG. 23 shows the geometry of the pole headingcorrection necessary in a moon attitude control. Herein A and Erepresent the azimuth and elevation of Polaris. A,,, and D, representthe azimuth and elevation of the moon after planet position computationhas been completed. T represents the desired angle of the axis of themoon from the local meridian. By spherical trigonometry i Referring toFIG. 24, the moon attitude control computer is shown. This consists ofresolver 192 into which a reference signal of standard size is fed. Theshaft of resolver 192 is positioned from the main star sphere at 90- 1The sine output of resolver 192 can then be fed into the resolver 194whose shaft position as derived from the star field represents theazimuth of the moon less the orientation of axis III (A 1 The sineoutput of resolver 194 together with the cosine output of resolver 192provide input signals to resolver 196 whose shaft position is 90 E,,,.The sine output of resolver 196 is fed as an input to resolver 198 as isthe cosine output of resolver 194. These two input signals combine andtogether with shaft position, which represents moon attitude position,produce an output. The output at thesine coil is fed to a signalamplifier 200 and operates the motor 202 which drives the shaft ofresolverl98 to the correct position to represent moon attitude, if notin that position. After the shaft reaches the position representingcorrect moon attitude, no further output will be produced. The shaft ofresolver 198 is therefore used to position the moon attitude controlapparatus.

The view of the moon, or the view of the earth, depends .moon line isrepresented as (I. The obtuse angle at which the line between the moonand the observer intersects the vernal :equinox line throughout theearth is identified as I V so that k the angle between the observersviewing position and the view of the moon as seen from earth becomes D-K. The means of obtaining the observers position in terms of x and y(ecliptic coordinates) has been shown in FIG. 19 and these coordinatescan be used as the input to the computer of FIG. 26 as they are derivedfrom the computer of FIG. 19 assuming the observer in the eclipticplane, i.e. z equals zero. The resolver 206 employs these coordinates asinput signals. With a shaft setting representing Q the output orresolver 206 is equal to sin l K) and cos I K). These two signals arethen used as the inputs of resolver 208 whose shaft position representsthe angle D -Q. Any signal at the sine output of resolver 208 is fed tosignal amplifier 210 which, in turn, feeds its signal to drive motor212. Motor 212, in turn, positions the shaft of resolver 208, ifnecessary. When the sine signal output of resolver 208 is eliminated,the shaft position remains fixed at what has thus been calculated to be(1),. g, the proper position for the moon view control. If no errorexists in the first place, no repositioning of the shaft of resolver 208will be necessary.

INTEGRATION OF PLANETARIUM COMPUTERS FIG. 27 shows in a highly schematicblock diagram the overall operation of the computer system controllingthe planetarium. In this diagram, the main star field projector and theindividual planet projectors are illustrated only as blocks. Itscomputers are similarly schematically represented as blocks and only thebroadest aspect of the interconnections of the operational componentsare suggested by connecting lines which are not intended to accuratelyrepresent electrical connections. The star field projector 4 iscontrolled under ordinary circumstances by a general rotation computer220, preferably of a type similar to that shown and described in mycopending application Ser. No. 356,093, suitable for simulation of dailyrotational motion of the star field about the pole of axis l or aboutany selected pole other than axis I. This computer, in short, makes itpossible to simulate daily motion as viewed from the surface of anotherplanet or vehicle or to simulate daily motion as viewed from the earthin another era in which the pole is shifted from Polaris.

In the event that axis I does not correspond to Polaris a correction isimposed on the general rotation computer by the axis I correctioncomputer 222. In the event that axis III is not vertical, andspecifically in the case where axis III is part of the 4 axis system ofFIG. 6, if the 4th axis is present still another computer 224 forcorrection of the position of the third axis is required. The computerhereinafter described is for the case in which axis III is in thereference meridian as defined. Of course, in a give system the thirdaxis computer 224 may feed directly into the general rotation computer220. In the event that it is desired to simulate pitch, roll and yaw, afurther computer 226 is required to feed the general rotation computer,either directly or through the chain of correction computers asrequired. The pitch, roll and yaw computer simulates conditions whichmight be experienced in a space craft and the amounts of these effectscan be selected, just as the parameters involved employed as inputs tothe other computers may be selected.

In addition to the computer inputs just described, manual inputs 228 areprovided to position the star field projector about the individual axesI, II and Ill and other axes, if employed, and to define the location ofthe staypole. These inputs may be automatically, as well as manually,adjusted in accordance with some predetermined program to simulateviewer reorientation anywhere in the solar system.

The planetarium star field projector 4 assumes positions in response tocommands from the computer and manual inputs and, as required, suppliesfeedback information on the positions assumed. The planetarium starfield projector also supplies information about the positions of itsaxis to the position computers as schematically indicated and aspreviously treated in some detail in connection with FIG. 18 forexample. The planet position computer reference to the star field isthus sensed by each of the computers 2305A, 2301, 230MA, 230V, 230MB,230E and 230SU.

These planet position computers, however, as previously described relyupon information from the coordinate conversion computers 2328A, 232],232MA, 232V, 232ME and 232E. As explained in some detail in connectionwith FIGS. 15, 16 and 17 vectorial sums are obtained through summingamplifiers 2348A, 2341, 234MA, 234V, 234MB, 234E and 234SU. The specificmanner of connection of the planet analogues to obtain the vectorialsums requires a selection of mode of operation which is accomplished byappropriate switching, schematically represented by switches 236, 237,

238, 239, 240, 241, 242, 243, 244 and 245 which, it will be understood.are intended to represent the ability to switch from one mode or viewpoint to another. Typical modes of operation are represented in FIGS.[5, l6 and I7 for certain limited numbers of bodies, by way of example.With more computer components the switching becomes more complex but theprinciple remains the same, With this vectorial information and the starfield orientation information, the planet position computers are ableto, in turn. appropriately direct their projectors SSA, 5.I, SMA, 5V, 5ME, SE and SSU to simulate appropriate selected positions of therespective planets and the sun on the planetarium dome. The positions ofthe planets will he understood to be changing with time in accordancewith input information to the planet coordinate conversion computerswhich, of course, must be programmed with appropriate informationrelative to one another.

The cis-luriar system is shown within dot and dashed box 250 andprovides its own earth projector SEA and moon projector 5M0, whichprojectors may be equipped with slides showing detail of the projectedbody and with zoom lenses to simulate size of the body dependent upondistance between the viewer and the body. The system also includes thevarious computers shown in FIGS. I9, 20, 22, 24 and 26. Thus, thegeneral observer coordinate conversion computer 232GB and the moon orsatellite computer 232M0 are fed to the earth position and the earthposition computer 252 and the moon position computer 254. respectively,through the means provided to convert from ecliptic'to equatorialcoordinants as shown in FIG. 19. Information from the earth positioncomputer 252 is, in turn, used to position the earth projector SEA, andinformation from the moon position computer is, in turn, used toposition the moon projector 5M0.

In order to convert the cis-lunar earth centered system into a suncentered system the converter 258 which corresponds to the computer ofFIG. 20 is employed to act upon the general observer coordinateconversion computer 23008. A moon phase control computer 260 similar tothat shown in FIG. 22 receives input information from the earthcoordinate conversion computer 232E and, in turn, provides an output foran adjustment for the phase control shutter of moon projector 5M0. Thesame or a similar control may be used to simulate earth phasing, shownhere as separate earth phase control 260' which acts upon the phasingshutter of the earth projector SEA. The moon attitude control 262receives information from moon position computer 254 to compute moonattitude which is used to adjust a slide or otherwise affect the moonprojector 5M0 in appropriate manner. Similarly, the earth attitudecomputer 262' receives an input from the earth position computer 252 aswell as the main star field or star sphere and its output is used toadjust a slide or otherwise simulate earth attitude in the earthprojector SEA. Finally, moon view control is accomplished by computer264 from the coordinate conversion computer input by way of moon viewcomputer 266. This, in turn, produces an output which adjusts the moonprojector 5M0 in accordance with appropriate moon view.

STAR FIELD PROJECTOR FIGS. 28a and 28b provide a pair of diagramsshowing the spherical geometry employed in order to better understandthe problem of positioning the star field projector, and in this casethe star sphere 10. FIG. 280 shows the geometry in the situation wherethe star field projector of FIG. 2 is involved.

In FIG. 280, are A is the angle between the zenith, which in this caseis coincident with axis Ill, and the staypole; are C is the anglebetween axis I at Polaris and the staypolc', and angle B is the anglebetween arcs A and C in the spherical triangle.

Angle B changes constantly in the course of simulation of daily motionbut arcs A and C remain the same. The angles 1%, 1 and '1 represent theangular settings of the respective axes I, II and III which are derivedby computer solution of the spherical triangle, given input; A, B and C.The heading H is the angle between a reference meridian and a greatcircle meridian through the staypole, and in this case, justed by axislll. 1

FIG. 28b shows the modified geometry when a star sphere projector havinga titled axis lll, like that of the projector of FIG. 6, is employedand/or a further modification of axis 1 location away from Polaris isemployed. Tl-le angles D,, 1 and 4 still represent the angular settingsof the respective axes l, ll and Ill. The reference meridian is definedby the zenith and the tilted axis lll. The heading H is the angle at thezenith between the reference meridian and the great circle connectingthe zenith and the staypole. Heading is no longer established directlyby movement of axis lll, but is a computed output resulting from theaction of theresolver chains on the heading input.

Are A* is the angle between axis lll tilted from the zenith M and thestaypole and is computed from the heading and the tilt of axis lll. ArcC* is the anglebetween the staypole and trans posed axis I at the samelocation other than through Polaris. Angle B* is the angle between thearcs Af" and C*. The changes in the locations of axes l and lll oreither of them accounts for the change in the triangle solved. lfsolution can be made of the triangle of FIG. 28a, 'shown in dot anddashed lines in FIG. 28b, then the general solution of any trianglehaving the vertices located by axesl and lll as shown in the solid linetriangle of FIG. 28b, can be obtained by superimposing conversioncomputers which effectively shift axis lll from the zenith M to itsselected tilted position and/or axis I from Polaris to any otherselected position. Thus in a shift ofaxis lll an input of A togetherwith inputs representative of tilt T and heading H will produce an Aoutput together with an increment of correction A.B to correct from B toB*. Similarly in a shift of axis I, an input of C together withdeclination of axis l and the difference in the right ascensions of thestaypole and axis I will produce C* output together with an increment ofcorrection A 8 to correct B to B*. The correction of B to B* willrequire both corrections of both axesare shifted, or the appropriate oneif only one axis is shifted. The axes once shifted will solve for theangles l and 1 of the solid line'triangle in FIG. 28!). Of course 1involves rotation about tilted axis lll; l rotation about shifted axis1; and 1 rotation about axis ll which is shifted with axis lll and whichis advantageously measured from shifted axis lll.

Referring now to FIG. 29, the block diagram is intended to show insomewhat greater detail the way in which the parameters of FIG. 28a andFIG. 28!) are used. Thus, it will be'seen the general rotation computer220 produces outputs to adjust the star field projector, star sphere 10,about axes I, ll and lll (and others which may be employed). Thisadjustment is coordinated with and relative to manual settings of theindividual axes through the manual input 228. The inputs into thegeneral rotation computer 220 are the parameters A*, B*, and C*. These,in turn, are derived from the axis l computer 222, axis computer 224 andpitch, roll and yaw computer 226. Any one of the computers 222, 224 and226 may be omitted and, if all are omitted, the inputs to the generalrotation computer are equal to A, B and C. In the event thataxis l isnot a Polaris staypole axis, inputs of the right ascension of thestaypole and the are C to the computer 222, which assumes that axis l ispreset at a codeclination C6,, andat a'right ascension raI, produceoutputs of C* and A 8. C* isthen fed directly to the general rotationcomputer and A 8 will be then fed to the summing differential oramplifier 268 to correct the reading of B to B*. lf only computer 222were employed, the A* input would equal A. Assuming that the axis lll isat an angle T with the zenith, the computer 224 is arrangedto receive aninput equal to A and one equal to H, the heading as defined in FIG. 288.The output of computer 224 is then A* which is fed directly to generalrotation computer 220 and AB which is fed together with the B signal tosumming differential or amplifier 268. If there is a A,B signal fromcomputer 222, it would also be fed to the summing differential oramplifier 268. Since the B, AB and A 8 outputs are normally shaftpositions a differential for summing them is the more obvious expedient,but

like D, is adit will be understood that using well known elements it ispossible to convert these mechanical to electrical signals to be summedin a suitable summing amplifier.

When pitch, roll and yaw are involved. the parameters A and B, as wellas the heading H, are modified and obtained as outputs from the computer226. If computer 224 is employed. the outputs A and H are fed to theinput ol'computer 224 and, if a manual H input is included as well, theseparate H inputs may be combined by suitable differential 225.Otherwise A may be fed directly to the general rotation computer. Eitherat the input to computer 224, as shown, if computer 224 is used orbefore general rotation computer 220 a suitable differential 227 may beused to combine the Hsignal from computer 226 with a manual A input. Bas an output from computer 226 is a varying component of v the B feddirectly to summing differential or amplifier 268 and together with theother B inputs to that component. The variable'voltage inputs to thepitch, roll and yaw computer are first'derivative with respect to time,Zliland Y, representing the rates of each of pitch, roll and yaw withrespect to time. These inputs are voltages each of which is selectedfrom a separate voltage divider calibrated directly in terms of rates ofpitch, roll or yaw. In the event computer 226 is used but there is noyaw input, a manual B input electrical signal may be substituted bysuitable switching. Similarly switching may be provided to permit anelectrical manual A input through computer 226. The elements shown asblocks in FIG. 29 are shown in FIGS. 30, 31, 32 and 33. FIG. 30 is thegeneral rotationcomputer of 220. FIG. 3! is the computer 222 having todo with the modified position of axis l. FIG. 32 is the computer 224having to'do with a shifted axis lll. FIG. 33 is pitch, roll and yawcomputer 226.

FlG. 30 corresponds to the general rotation computer shown and describedin my U..S. Pat. No. 3,256,619 with modifications to make it moresuitable with the illustrated embodiment of the present invention. Theresolvers 270 and 272 have their shafts set to represent the angle A.The resolvers 274 and 276 have their shafts set to represent the angleB*. and the resolvers 278 and 280 have their shafts set to represent C*.The resolvers, except for common shaft positioning, from two separatechains. The upper chain produces outputs representative of the angles 1and Ll and the lower chain produces an output representative of theangle 4 With inputs'A B* and C*. using a fixed reference input signal,the desired output angles necessary to position the star field projectorare provided. As previously stated, if axis lll is not tilted, then A*is equal to A and represents observer latitude. lf axis 1 extendsthrough Polaris, then C represents the angle between the Polaris and thechosen staypole or what would normally be C. B* is equal to B only ifaxis lll is not tilted and axis 1 extends through Polaris except in theunique case where both Polaris and the staypole are on the referencemeridian. In the course of a planetarium lecture describing dailyrotation of the star field, 8* is varied to indicate the daily rotationof the star field about the selected pole star and the computer of FIG.30 calculates and supplies the correct angular positioning for thisoperation at axis l, II and lll. In the event that the axes l and lllare respectively noncoincident with Polaris and the zenith, then A", B*and C* are no longer the terms defined but are modified terms stillnecessary to calculate the required axial positioning of axis I, ll andlll.

A fixed reference voltage applied at resolver 280 produces sin C and cosC outputs, the former being fed to resolver 276 and the cos C outputfrom resolver 280 are used as inputs to resolver 272 and, in turn,produce the trigonometric output functions shown on the drawing. Theoutput of resolver 272 fed to resolver I7 is the equivalent of cos l sin1 whereas the output of resolver 276 fed to resolver i7 is equivalent tosin 1 sin D Combining these two inputs to resolver l7 enables one outputto servoamplifier 288 which is a function of angle 1 to drive the motor15 until its shaft which is connected to the shaft of resolver 17 isrepresentative of the angle 1 at which point there is no further outputsignal through amplifier 288. The other output from resolver 17 isrepresen-

1. A planetarium system comprising a screen, a star field projector forprojecting any selected portion of the celestial sphere in any desiredorientation upon said screen, sun, moon and planet image directingprojectors, each mounted separately from one another and from the starfield projector, each independently movable with respect to one anotherand with respect to the star field projector and universally movablewithin a range necessary to cover the screen so that the orbit of theprojected body can be accurately reproduced upon said screen to simulatea viewer position any place in solar system space, each projecting animage point of light small with respect to the projected star field of aselected body and each having suitable drive means permitting movementof the projector for the reqUired simulation of movement of the bodywhose image it projects relative to and through the projected star fieldon the screen and a computer link coupling the various sun, moon andplanet projectors to the star field projector and providing signals tothe drive means of the respective projectors such that the projectedimages of the sun, moon and planets will respectively assume properpositions and follow proper orbits relative to the star filed for afixed or moving viewer position within the solar system.
 2. Theplanetarium of claim 1 in which the computer vectorially sums thepositions relative to the star field reference frame of each of theviewed bodies and a selected viewer position to derive a line of sightvector along which the projector for projecting that particular viewedbody is directed.
 3. The planetarium of claim 1 in which the computer islocated remotely from the projector and the only links between theprojector and the computer are electrical leads.
 4. The planetarium ofclaim 1 in which the star field projector is provided with at leastthree axes of rotational movement to permit essentially universalrotational positioning of the star field and at least means for sensingits position and orientation is coupled to the computer.
 5. Theplanetarium of claim 4 in which the planet projectors are capable ofbeing moved in patterns of movement to simulate variable viewer positionand in which means is provided to produce variation of the viewerposition in accordance with an operator predetermined program. 6, Theplanetarium of claim 5 in which the planet projectors are capable ofbeing moved in patterns of movement to simulate viewer positionselectable as a nonrecurring pattern and may include regions outside ofthe general plane of the ecliptic.
 7. A planetarium system comprising ascreen in the form of a portion of a sphere, a star field projectorcapable of projecting any selected portion of the celestial sphere inany desired orientation upon said screen, at least four planetprojectors independent of the star field and each projecting an imagesmall with respect to the projected star field representing a planetwhich moves relative to and through the projected star field on thescreen and including suitable drive means permitting the movement forthe required simulation of movement of the body whose image it projects,and a computer link coupling the projectors and causing the drive meansof each projector to assume successive predetermined positions such thatthe image projected will follow paths through the star field necessaryto simulate the orbits of the selected planets as viewed from anyselected fixed or moving viewer position within the solar system.
 8. Theplanetarium of claim 7 in which the computer vectorially sums thepositions relative to the star field reference frame of the celestialbody whose image is projected by the projector and a selected viewerposition to derive a line of sight vector along which the projector isdirected.
 9. The planetarium of claim 7 in which the computer is locatedremotely from the projector and the only links between the projector andthe computer are electrical leads.
 10. The planetarium of claim 7 inwhich the star field projector is provided with at least three axes ofrotational movement to permit essentially universal rotationalpositioning of the star field and at least means for sensing itsposition is coupled to the computer.
 11. The planetarium of claim 10wherein the projectors have sufficient positionability to simulate acondition in which viewer position is variable and in which means isprovided to produce variation of the viewer position in accordance withan operator predetermined program.
 12. The planetarium of claim 11 inwhich the planet projectors are capable of being moved in patterns ofmovement to simulate viewer position selectable as a nonrecurringpattern and may include regions outside of the general plane of theecliptic.
 13. A planetarium system comprising a generally sphericallycurved projection screen, a star field projector capable of projectingany selected portion of the celestial sphere in any desired orientationupon said screen, at least four planet projectors located remotely fromthe star field projector and away from the center of the projectionscreen for projecting images small with respect to the projected starfield and each representing a planet which moves relative to and throughthe projected star field on the screen and including suitable drivemeans permitting the movement for the required simulation of movement ofthe body whose image it projects, a computer link coupling theprojectors and causing the drive means of each projector to assumesuccessive predetermined positions such that the image projected willfollow paths through the star field necessary to simulate the orbits ofthe selected planets as viewed from any selected fixed or moving viewerposition within the solar system, and correction means for each planetprojector to adjust its image position on said screen in proportion tothe offset of the projector from the center of the projection screen.14. A planetarium system comprising a generally spherical projectiondome, a star field projector capable of projecting any selected portionof the celestial sphere in any desired orientation onto said dome, atleast four planet projectors for projecting images small with respect tothe projected star field of other natural or artificial celestialbodies, each mounted independently of the others and of the star fieldprojector and capable of of positioning independently of otherprojectors to project images of their respective planets within andmoving through the star field universally over said dome, means,including drive means, for selectively positioning each of the planetprojectors relative to the star field projector and computer meansresponsive to star field position to generate signals in accordance withprogramming information supplied to the computer for properlypositioning images from each of said planet projectors relative to thestar field.
 15. The planetarium system of claim 14 in which drive meansis provided for selectively positioning the star field projector. 16.The planetarium system of claim 15 in which each of said otherprojectors is vectorially directed by a computer in a directiondescribed by a vectorial summation of viewer position and the viewedplanet position.
 17. The planetarium system of claim 15 in which each ofsaid other projectors is vectorially directed by a computer in adirection described by the difference between the viewer position andthe viewed planet position.
 18. In a planetarium system, a positioncomputer for a viewed point whose position in the star field is known interms of star field components comprising means to generate coordinatesof the viewed point in the star field, coordinate conversion means toconvert said coordinates to planetarium coordinates having an inputcoupled to the means to generate coordinates, and viewed pointprojection means including motor means coupled to the coordinateconversion means to position the projection means such that the viewedpoint projected by it will fall in the proper position in the starfield.
 19. The position computer for a viewed point of claim 18 in whichthe motor means coupled to the coordinate conversion means to positionthe projection means consists of separate motor means which respectivelyadjust the azimuth and elevation of the projection means in the viewedpoint projection means in response to signals representative of saidadjustment.
 20. The position computer for a viewed point of claim 19 inwhich each motor means is part of a signal nulling servoloop whichcorrects projector position as the position of the viewed point changes.21. A view control for a planetarium moon or earth projector comprisingsignal generating means to generate an output representative of earthpositiOn relative to an observer in cis-lunar space, means to generatean output representative of moon position relative to the earth incis-lunar space, computer means receiving said outputs from theaforesaid means as inputs and producing therefrom an output signalrepresentative of moon or earth view from observer positions, and meanscooperative with the moon or earth projector for simulating moon orearth view coupled to the computer means and response to the outputsignal therefrom to position the moon or earth view simulating means.22. The view control of claim 21 in which the means to position the moonor earth view simulating means includes servomotor means in a nullfeedback loop to correct moon or earth phasing automatically as relativepositions of the moon or earth and the observer change.
 23. Theplanetarium system of claim 13 in which the connection means iselectrical means whereby an electrical signal may be inserted into thecomputer link to correct for the offcenter position of the projector.